Textbook Problem

Let S be the set of all strings of $a\text{'}s$ and $b\text{'}s.$

1. Define $f:S\to Z$as follows: For each string s in S
   $f\left(s\right)=\{\begin{array}{c}\text{the}\text{number}\text{of}b\text{'}s\text{to}\text{the}\text{left}\\ \text{of}\text{the}\text{left-most}a\text{in}s\\ 0\text{if}s\text{contains}\text{no}a\text{'}s.\end{array}$

Find $f\left(aba\right),f\left(bbab\right),$ and  $f\left(b\right).$ What is the range of f?

Define $g:S\to S$as follows: For each string s in S.

$g\left(s\right)=$  the string obtained by writing the characters of s in reverse order.
Find $g\left(aba\right),g\left(bbab\right),$ and $g\left(b\right).$ What is the range of g?